A variety of different feedback control systems are known, including on-off control and proportional (P) control in which the controller output is proportional to the error between the system set point and the measured system output.
A problem with proportional control systems is that they can tend to oscillate and that the control output is always in direct proportion to the error. To resolve these problems and others many feedback control schemes include mathematical extensions to improve performance. The most common extensions are proportional-integral-derivative (PID) type control systems.
In PID control systems, the derivative (D) part is concerned with the rate-of-change of the error with time: If the measured variable approaches the setpoint rapidly, then the actuator is backed off early to allow it to coast to the required level. Derivative action makes a control system behave much more intelligently. The integral (I) term magnifies the effect of long-term steady-state errors, applying ever-increasing effort until they reduce to zero. In a PID controller, separate parameters for the P, I and D elements are employed. Typically, these parameters would be determined at a design stage or during an initial commissioning of a control system. A difficulty with these systems is that whilst the determined parameters for a PID controller might be optimum at the time of commissioning or design of a controller, the characteristics of a system may change over time. In other cases, the characteristics of the system may only be known with a low accuracy, and therefore controller design is likely to be suboptimal.
To address this, adaptive control may be employed. Generally, adaptive control relies upon determination of a system's characteristics and designing the correct controller for these characteristics. Suitably, the determination of the system characteristics and the design of the controller happens in real-time and on-the-fly as the system is running. In general there are two methods of adaptive control which differ according to how the system parameters are estimated: Parametric and Non Parametric
Non-Parametric methods estimate the system parameters by measuring something about the system such as its step response or frequency response, and then employ this data to design the correct controller. On the positive side, these methods are relatively non-complex and intuitive. However, on the negative side they are known to be sensitive to noise, interference and other non-idealities which can make for a poor controller design, and they cannot work on-line continuously because you need to make the required measurements to determine the system parameters. A basic prior art non-parametric method is illustrated in FIG. 1. In this scheme the system is subject to relay control during a calibration cycle, where key parameters of the loop are determined. In common with non-parametric methods in general, this method has several drawbacks including that the regulation of the loop is disturbed during the tuning procedure. The identification of high frequency characteristics is sensitive to noise and therefore the method is inaccurate in the most important frequency range.
Parametric methods incorporate a model of the system and estimate the correct system parameters using adaptive methods. On the positive side, this method can work on-line and is insensitive to noise. But on the negative side, it's very complex and costly to implement as the computing power required to perform the calculations on a fast process would be expensive. As a result, parametric methods are generally employed in slower systems and thus for example are popular in process control, e.g. in chemical plants where the system response times may be minutes or hours rather than fractions of a second.
The parametric method will now be described with reference to an exemplary self-tuning regulator 10, shown in FIG. 2, consisting of a controller 12 and a plant 14, whereby the parameters of the plant are estimated by the ‘plant parameter estimation’ block 16. The estimated parameters are used as inputs to the ‘controller design’ block, to determine the correct parameters for the controller. The estimation of plant parameters is a system identification problem.
System identification is broadly concerned with modelling dynamic systems using measured experimental data. In general terms system identification relies upon parameter estimation which may employ parametric or non-parametric methods. Parametric methods require an adaptive filter for implementation.
Parameter estimation is a fundamental part of system identification. It uses a model to relate the measured data to the unknown parameters. The general relationship, where w is a vector of unknown parameters, u(n) is a vector of data applied to the system, and y(n) is the output is shown in equation (1):y(n)=u(n)w  (1)
The model used for parameter estimation does not need to be the same as the control model. The only requirement is that the measured data is linearly related to the parameters via the model. Re-parameterisation of the model is possible by applying a stable filter to both the input and output data. Any linear system can be written as equation (1) using this method of re-parameterisation. This method underlies the formulation of the direct form of the self-tuning regulator described above.
The goal of the parameter estimation algorithm is to minimise the prediction error, i.e. the difference between the estimated values of the output of the system and the actual values.
This is achieved by modifying the parameter estimates iteratively so as to minimise the prediction error so that the parameters of the estimator and the Plant ultimately match. The operation is illustrated in FIG. 3, where the plant 24 and the estimator 26 are driven by the same signal u(n). The desired response of the estimator designated y(n), is the same as the plant in this case (though it need not be). The estimation error pe(n) is simply the difference between the desired response y(n) and the actual response of the estimator ŷ(n).
Methods for implementing the parameter estimator and the mechanism 28 for updating the parameters come from the field of adaptive filter design.
Practical online adaptive controllers such as the self-tuning regulator have relied upon parameter estimation to identify the parameters of the plant, operating under the assumption of certainty equivalence, whereby the estimated plant parameters are treated as the true values for the purposes of controller design. Such an approach requires accurate estimation, in the shortest possible time, and therefore requires computationally complex adaptive filters. Accordingly, this makes the traditional approach unsuitable for a low-cost control applications.
The present application seeks to provide an adaptive control method which employs a parametric type approach which is suitable for low-cost control applications.
The present application is therefore directed towards providing an improved control system addressing at least some of the above problems.